/* $Id$ */ # ifndef CPPAD_OLD_ATOMIC_INCLUDED # define CPPAD_OLD_ATOMIC_INCLUDED /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-14 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the GNU General Public License Version 3. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ /* $begin old_atomic$$ $spell hes std Jacobian jac Tvector afun vx vy bool namespace CppAD const Taylor tx ty px py $$ $section User Defined Atomic AD Functions$$ $index CPPAD_USER_ATOMIC$$ $index atomic, user function$$ $index user, atomic function$$ $index operation, user atomic$$ $index function, user atomic$$ $head Syntax$$ Using $code CPPAD_USER_ATOMIC$$ has been deprecated. Use $cref atomic_base$$ instead. $subhead Define Function$$ $codei%CPPAD_USER_ATOMIC(%afun%, %Tvector%, %Base%, %forward%, %reverse%, %for_jac_sparse%, %rev_jac_sparse%, %rev_hes_sparse% ) %$$ $subhead Use Function$$ $icode%afun%(%id%, %ax%, %ay%) %$$ $subhead Callback Routines$$ $icode%ok% = %forward%(%id%, %k%, %n%, %m%, %vx%, %vy%, %tx%, %ty%) %$$ $icode%ok% = %reverse%(%id%, %k%, %n%, %m%, %tx%, %ty%, %px%, %py%) %$$ $icode%ok% = %for_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ $icode%ok% = %rev_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ $icode%ok% = %rev_hes_sparse%(%id%, %n%, %m%, %q%, %r%, %s%, %t%, %u%, %v%) %$$ $subhead Free Static Memory$$ $codei%user_atomic<%Base%>::clear()%$$ $head Purpose$$ In some cases, the user knows how to compute the derivative of a function $latex \[ y = f(x) \; {\rm where} \; f : B^n \rightarrow B^m \] $$ more efficiently than by coding it using $codei%AD<%Base%>%$$ $cref/atomic/glossary/Operation/Atomic/$$ operations and letting CppAD do the rest. In this case, $code CPPAD_USER_ATOMIC$$ can be used add the user code for $latex f(x)$$, and its derivatives, to the set of $codei%AD<%Base%>%$$ atomic operations. $pre $$ Another possible purpose is to reduce the size of the tape; see $cref/use AD/old_atomic/Example/Use AD/$$ $head Partial Implementation$$ The routines $cref/forward/old_atomic/forward/$$, $cref/reverse/old_atomic/reverse/$$, $cref/for_jac_sparse/old_atomic/for_jac_sparse/$$, $cref/rev_jac_sparse/old_atomic/rev_jac_sparse/$$, and $cref/rev_hes_sparse/old_atomic/rev_hes_sparse/$$, must be defined by the user. The $icode forward$$ the routine, for the case $icode%k% = 0%$$, must be implemented. Functions with the correct prototype, that just return $code false$$, can be used for the other cases (unless they are required by your calculations). For example, you need not implement $icode forward$$ for the case $icode%k% == 2%$$ until you require forward mode calculation of second derivatives. $head CPPAD_USER_ATOMIC$$ $index CPPAD_USER_ATOMIC$$ The macro $codei% CPPAD_USER_ATOMIC(%afun%, %Tvector%, %Base%, %forward%, %reverse%, %for_jac_sparse%, %rev_jac_sparse%, %rev_hes_sparse% ) %$$ defines the $codei%AD<%Base%>%$$ routine $icode afun$$. This macro can be placed within a namespace (not the $code CppAD$$ namespace) but must be outside of any routine. $subhead Tvector$$ The macro argument $icode Tvector$$ must be a $cref/simple vector template class/SimpleVector/$$. It determines the type of vectors used as arguments to the routine $icode afun$$. $subhead Base$$ The macro argument $icode Base$$ specifies the $cref/base type/base_require/$$ corresponding to $codei%AD<%Base>%$$ operation sequences. Calling the routine $icode afun$$ will add the operator defined by this macro to an $codei%AD<%Base>%$$ operation sequence. $head ok$$ For all routines documented below, the return value $icode ok$$ has prototype $codei% bool %ok% %$$ If it is $code true$$, the corresponding evaluation succeeded, otherwise it failed. $head id$$ For all routines documented below, the argument $icode id$$ has prototype $codei% size_t %id% %$$ Its value in all other calls is the same as in the corresponding call to $icode afun$$. It can be used to store and retrieve extra information about a specific call to $icode afun$$. $head k$$ For all routines documented below, the argument $icode k$$ has prototype $codei% size_t %k% %$$ The value $icode%k%$$ is the order of the Taylor coefficient that we are evaluating ($cref/forward/old_atomic/forward/$$) or taking the derivative of ($cref/reverse/old_atomic/reverse/$$). $head n$$ For all routines documented below, the argument $icode n$$ has prototype $codei% size_t %n% %$$ It is the size of the vector $icode ax$$ in the corresponding call to $icode%afun%(%id%, %ax%, %ay%)%$$; i.e., the dimension of the domain space for $latex y = f(x)$$. $head m$$ For all routines documented below, the argument $icode m$$ has prototype $codei% size_t %m% %$$ It is the size of the vector $icode ay$$ in the corresponding call to $icode%afun%(%id%, %ax%, %ay%)%$$; i.e., the dimension of the range space for $latex y = f(x)$$. $head tx$$ For all routines documented below, the argument $icode tx$$ has prototype $codei% const CppAD::vector<%Base%>& %tx% %$$ and $icode%tx%.size() >= (%k% + 1) * %n%$$. For $latex j = 0 , \ldots , n-1$$ and $latex \ell = 0 , \ldots , k$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} x_j^\ell & = & tx [ j * ( k + 1 ) + \ell ] \\ X_j (t) & = & x_j^0 + x_j^1 t^1 + \cdots + x_j^k t^k \end{array} \] $$ If $icode%tx%.size() > (%k% + 1) * %n%$$, the other components of $icode tx$$ are not specified and should not be used. Note that superscripts represent an index for $latex x_j^\ell$$ and an exponent for $latex t^\ell$$. Also note that the Taylor coefficients for $latex X(t)$$ correspond to the derivatives of $latex X(t)$$ at $latex t = 0$$ in the following way: $latex \[ x_j^\ell = \frac{1}{ \ell ! } X_j^{(\ell)} (0) \] $$ $head ty$$ In calls to $cref/forward/old_atomic/forward/$$, the argument $icode ty$$ has prototype $codei% CppAD::vector<%Base%>& %ty% %$$ while in calls to $cref/reverse/old_atomic/reverse/$$ it has prototype $codei% const CppAD::vector<%Base%>& %ty% %$$ For all calls, $icode%tx%.size() >= (%k% + 1) * %m%$$. For $latex i = 0 , \ldots , m-1$$ and $latex \ell = 0 , \ldots , k$$, we use the Taylor coefficient notation $latex \[ \begin{array}{rcl} y_i^\ell & = & ty [ i * ( k + 1 ) + \ell ] \\ Y_i (t) & = & y_i^0 + y_i^1 t^1 + \cdots + y_i^k t^k + o ( t^k ) \end{array} \] $$ where $latex o( t^k ) / t^k \rightarrow 0$$ as $latex t \rightarrow 0$$. If $icode%ty%.size() > (%k% + 1) * %m%$$, the other components of $icode ty$$ are not specified and should not be used. Note that superscripts represent an index for $latex y_j^\ell$$ and an exponent for $latex t^\ell$$. Also note that the Taylor coefficients for $latex Y(t)$$ correspond to the derivatives of $latex Y(t)$$ at $latex t = 0$$ in the following way: $latex \[ y_j^\ell = \frac{1}{ \ell ! } Y_j^{(\ell)} (0) \] $$ $subhead forward$$ In the case of $icode forward$$, for $latex i = 0 , \ldots , m-1$$, $latex ty[ i *( k + 1) + k ]$$ is an output and all the other components of $icode ty$$ are inputs. $subhead reverse$$ In the case of $icode reverse$$, all the components of $icode ty$$ are inputs. $head afun$$ The macro argument $icode afun$$, is the name of the AD function corresponding to this atomic operation (as it is used in the source code). CppAD uses the other functions, where the arguments are vectors with elements of type $icode Base$$, to implement the function $codei% %afun%(%id%, %ax%, %ay%) %$$ where the argument are vectors with elements of type $codei%AD<%Base%>%$$. $subhead ax$$ The $icode afun$$ argument $icode ax$$ has prototype $codei% const %Tvector%< AD<%Base%> >& %ax% %$$ It is the argument vector $latex x \in B^n$$ at which the $codei%AD<%Base%>%$$ version of $latex y = f(x)$$ is to be evaluated. The dimension of the domain space for $latex y = f (x)$$ is specified by $cref/n/old_atomic/n/$$ $codei%= %ax%.size()%$$, which must be greater than zero. $subhead ay$$ The $icode afun$$ result $icode ay$$ has prototype $codei% %Tvector%< AD<%Base%> >& %ay% %$$ The input values of its elements are not specified (must not matter). Upon return, it is the $codei%AD<%Base%>%$$ version of the result vector $latex y = f(x)$$. The dimension of the range space for $latex y = f (x)$$ is specified by $cref/m/old_atomic/m/$$ $codei%= %ay%.size()%$$, which must be greater than zero. $subhead Parallel Mode$$ $index parallel, old_atomic$$ $index old_atomic, parallel$$ The first call to $codei% %afun%(%id%, %ax%, %ay%) %$$ must not be in $cref/parallel/ta_in_parallel/$$ mode. In addition, the $cref/old_atomic clear/old_atomic/clear/$$ routine cannot be called while in parallel mode. $head forward$$ The macro argument $icode forward$$ is a user defined function $codei% %ok% = %forward%(%id%, %k%, %n%, %m%, %vx%, %vy%, %tx%, %ty%) %$$ that computes results during a $cref/forward/Forward/$$ mode sweep. For this call, we are given the Taylor coefficients in $icode tx$$ form order zero through $icode k$$, and the Taylor coefficients in $icode ty$$ with order less than $icode k$$. The $icode forward$$ routine computes the $icode k$$ order Taylor coefficients for $latex y$$ using the definition $latex Y(t) = f[ X(t) ]$$. For example, for $latex i = 0 , \ldots , m-1$$, $latex \[ \begin{array}{rcl} y_i^0 & = & Y(0) = f_i ( x^0 ) \\ y_i^1 & = & Y^{(1)} ( 0 ) = f_i^{(1)} ( x^0 ) X^{(1)} ( 0 ) = f_i^{(1)} ( x^0 ) x^1 \\ y_i^2 & = & \frac{1}{2 !} Y^{(2)} (0) \\ & = & \frac{1}{2} X^{(1)} (0)^\R{T} f_i^{(2)} ( x^0 ) X^{(1)} ( 0 ) + \frac{1}{2} f_i^{(1)} ( x^0 ) X^{(2)} ( 0 ) \\ & = & \frac{1}{2} (x^1)^\R{T} f_i^{(2)} ( x^0 ) x^1 + f_i^{(1)} ( x^0 ) x^2 \end{array} \] $$ Then, for $latex i = 0 , \ldots , m-1$$, it sets $latex \[ ty [ i * (k + 1) + k ] = y_i^k \] $$ The other components of $icode ty$$ must be left unchanged. $subhead Usage$$ This routine is used, with $icode%vx%.size() > 0%$$ and $icode%k% == 0%$$, by calls to $icode afun$$. It is used, with $icode%vx%.size() = 0%$$ and $icode k$$ equal to the order of the derivative begin computed, by calls to $cref/forward/forward_order/$$. $subhead vx$$ The $icode forward$$ argument $icode vx$$ has prototype $codei% const CppAD::vector& %vx% %$$ The case $icode%vx%.size() > 0%$$ occurs once for each call to $icode afun$$, during the call, and before any of the other callbacks corresponding to that call. Hence such a call can be used to cache information attached to the corresponding $icode id$$ (such as the elements of $icode vx$$). If $icode%vx%.size() > 0%$$ then $icode%k% == 0%$$, $icode%vx%.size() >= %n%$$, and for $latex j = 0 , \ldots , n-1$$, $icode%vx%[%j%]%$$ is true if and only if $icode%ax%[%j%]%$$ is a $cref/variable/glossary/Variable/$$. $pre $$ If $icode%vx%.size() == 0%$$, then $icode%vy%.size() == 0%$$ and neither of these vectors should be used. $subhead vy$$ The $icode forward$$ argument $icode vy$$ has prototype $codei% CppAD::vector& %vy% %$$ If $icode%vy%.size() == 0%$$, it should not be used. Otherwise, $icode%k% == 0%$$ and $icode%vy%.size() >= %m%$$. The input values of the elements of $icode vy$$ are not specified (must not matter). Upon return, for $latex j = 0 , \ldots , m-1$$, $icode%vy%[%i%]%$$ is true if and only if $icode%ay%[%j%]%$$ is a variable. (CppAD uses $icode vy$$ to reduce the necessary computations.) $head reverse$$ The macro argument $icode reverse$$ is a user defined function $codei% %ok% = %reverse%(%id%, %k%, %n%, %m%, %tx%, %ty%, %px%, %py%) %$$ that computes results during a $cref/reverse/Reverse/$$ mode sweep. The input value of the vectors $icode tx$$ and $icode ty$$ contain Taylor coefficient, up to order $icode k$$, for $latex X(t)$$ and $latex Y(t)$$ respectively. We use the $latex \{ x_j^\ell \}$$ and $latex \{ y_i^\ell \}$$ to denote these Taylor coefficients where the implicit range indices are $latex i = 0 , \ldots , m-1$$, $latex j = 0 , \ldots , n-1$$, $latex \ell = 0 , \ldots , k$$. Using the calculations done by $cref/forward/old_atomic/forward/$$, the Taylor coefficients $latex \{ y_i^\ell \}$$ are a function of the Taylor coefficients for $latex \{ x_j^\ell \}$$; i.e., given $latex y = f(x)$$ we define the function $latex F : B^{n \times (k+1)} \rightarrow B^{m \times (k+1)}$$ by $latex \[ y_i^\ell = F_i^\ell ( \{ x_j^\ell \} ) \] $$ We use $latex G : B^{m \times (k+1)} \rightarrow B$$ to denote an arbitrary scalar valued function of the Taylor coefficients for $latex Y(t)$$ and write $latex z = G( \{ y_i^\ell \} )$$. The $code reverse$$ routine is given the derivative of $latex z$$ with respect to $latex \{ y_i^\ell \}$$ and computes its derivative with respect to $latex \{ x_j^\ell \}$$. $subhead Usage$$ This routine is used, with $icode%k% + 1%$$ equal to the order of the derivative being calculated, by calls to $cref/reverse/reverse_any/$$. $subhead py$$ The $icode reverse$$ argument $icode py$$ has prototype $codei% const CppAD::vector<%Base%>& %py% %$$ and $icode%py%.size() >= (%k% + 1) * %m%$$. For $latex i = 0 , \ldots , m-1$$ and $latex \ell = 0 , \ldots , k$$, $latex \[ py[ i * (k + 1 ) + \ell ] = \partial G / \partial y_i^\ell \] $$ If $icode%py%.size() > (%k% + 1) * %m%$$, the other components of $icode py$$ are not specified and should not be used. $subhead px$$ We define the function $latex \[ H ( \{ x_j^\ell \} ) = G[ F( \{ x_j^\ell \} ) ] \] $$ The $icode reverse$$ argument $icode px$$ has prototype $codei% CppAD::vector<%Base%>& %px% %$$ and $icode%px%.size() >= (%k% + 1) * %n%$$. The input values of the elements of $icode px$$ are not specified (must not matter). Upon return, for $latex j = 0 , \ldots , n-1$$ and $latex p = 0 , \ldots , k$$, $latex \[ \begin{array}{rcl} px [ j * (k + 1) + p ] & = & \partial H / \partial x_j^p \\ & = & ( \partial G / \partial \{ y_i^\ell \} ) ( \partial \{ y_i^\ell \} / \partial x_j^p ) \\ & = & \sum_{i=0}^{m-1} \sum_{\ell=0}^k ( \partial G / \partial y_i^\ell ) ( \partial y_i^\ell / \partial x_j^p ) \\ & = & \sum_{i=0}^{m-1} \sum_{\ell=p}^k py[ i * (k + 1 ) + \ell ] ( \partial F_i^\ell / \partial x_j^p ) \end{array} \] $$ Note that we have used the fact that for $latex \ell < p$$, $latex \partial F_i^\ell / \partial x_j^p = 0$$. If $icode%px%.size() > (%k% + 1) * %n%$$, the other components of $icode px$$ are not specified and should not be used. $head for_jac_sparse$$ The macro argument $icode for_jac_sparse$$ is a user defined function $codei% %ok% = %for_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ that is used to compute results during a forward Jacobian sparsity sweep. For a fixed $latex n \times q$$ matrix $latex R$$, the Jacobian of $latex f( x + R * u)$$ with respect to $latex u \in B^q$$ is $latex \[ S(x) = f^{(1)} (x) * R \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex R$$, $icode for_jac_sparse$$ computes a sparsity pattern for $latex S(x)$$. $subhead Usage$$ This routine is used by calls to $cref ForSparseJac$$. $subhead q$$ The $icode for_jac_sparse$$ argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in $latex R \in B^{n \times q}$$ and the Jacobian $latex S(x) \in B^{m \times q}$$. $subhead r$$ The $icode for_jac_sparse$$ argument $icode r$$ has prototype $codei% const CppAD::vector< std::set >& %r% %$$ and $icode%r%.size() >= %n%$$. For $latex j = 0 , \ldots , n-1$$, all the elements of $icode%r%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex R$$. $subhead s$$ The $icode for_jac_sparse$$ return value $icode s$$ has prototype $codei% CppAD::vector< std::set >& %s% %$$ and $icode%s%.size() >= %m%%$$. The input values of its sets are not specified (must not matter). Upon return for $latex i = 0 , \ldots , m-1$$, all the elements of $icode%s%[%i%]%$$ are between zero and $icode%q%-1%$$ inclusive. This represents a sparsity pattern for the matrix $latex S(x)$$. $head rev_jac_sparse$$ The macro argument $icode rev_jac_sparse$$ is a user defined function $codei% %ok% = %rev_jac_sparse%(%id%, %n%, %m%, %q%, %r%, %s%) %$$ that is used to compute results during a reverse Jacobian sparsity sweep. For a fixed $latex q \times m$$ matrix $latex S$$, the Jacobian of $latex S * f( x )$$ with respect to $latex x \in B^n$$ is $latex \[ R(x) = S * f^{(1)} (x) \] $$ Given a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for $latex S$$, $icode rev_jac_sparse$$ computes a sparsity pattern for $latex R(x)$$. $subhead Usage$$ This routine is used by calls to $cref RevSparseJac$$ and to $cref optimize$$. $subhead q$$ The $icode rev_jac_sparse$$ argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of rows in $latex S \in B^{q \times m}$$ and the Jacobian $latex R(x) \in B^{q \times n}$$. $subhead s$$ The $icode rev_jac_sparse$$ argument $icode s$$ has prototype $codei% const CppAD::vector< std::set >& %s% %$$ and $icode%s%.size() >= %m%$$. For $latex i = 0 , \ldots , m-1$$, all the elements of $icode%s%[%i%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex S^\R{T}$$. $subhead r$$ The $icode rev_jac_sparse$$ return value $icode r$$ has prototype $codei% CppAD::vector< std::set >& %r% %$$ and $icode%r%.size() >= %n%$$. The input values of its sets are not specified (must not matter). Upon return for $latex j = 0 , \ldots , n-1$$, all the elements of $icode%r%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This represents a sparsity pattern for the matrix $latex R(x)^\R{T}$$. $head rev_hes_sparse$$ The macro argument $icode rev_hes_sparse$$ is a user defined function $codei% %ok% = %rev_hes_sparse%(%id%, %n%, %m%, %q%, %r%, %s%, %t%, %u%, %v%) %$$ There is an unspecified scalar valued function $latex g : B^m \rightarrow B$$. Given a sparsity pattern for $latex R$$ and information about the function $latex z = g(y)$$, this routine computes the sparsity pattern for $latex \[ V(x) = (g \circ f)^{(2)}( x ) R \] $$ $subhead Usage$$ This routine is used by calls to $cref RevSparseHes$$. $subhead q$$ The $icode rev_hes_sparse$$ argument $icode q$$ has prototype $codei% size_t %q% %$$ It specifies the number of columns in the sparsity patterns. $subhead r$$ The $icode rev_hes_sparse$$ argument $icode r$$ has prototype $codei% const CppAD::vector< std::set >& %r% %$$ and $icode%r%.size() >= %n%$$. For $latex j = 0 , \ldots , n-1$$, all the elements of $icode%r%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex R \in B^{n \times q}$$. $subhead s$$ The $icode rev_hes_sparse$$ argument $icode s$$ has prototype $codei% const CppAD::vector& %s% %$$ and $icode%s%.size() >= %m%$$. This specifies a sparsity pattern for the matrix $latex S(x) = g^{(1)} (y) \in B^{1 \times m}$$. $subhead t$$ The $icode rev_hes_sparse$$ argument $icode t$$ has prototype $codei% CppAD::vector& %t% %$$ and $icode%t%.size() >= %n%$$. The input values of its elements are not specified (must not matter). Upon return it represents a sparsity pattern for the matrix $latex T(x) \in B^{1 \times n}$$ defined by $latex \[ T(x) = (g \circ f)^{(1)} (x) = S(x) * f^{(1)} (x) \] $$ $subhead u$$ The $icode rev_hes_sparse$$ argument $icode u$$ has prototype $codei% const CppAD::vector< std::set >& %u% %$$ and $icode%u%.size() >= %m%$$. For $latex i = 0 , \ldots , m-1$$, all the elements of $icode%u%[%i%]%$$ are between zero and $icode%q%-1%$$ inclusive. This specifies a sparsity pattern for the matrix $latex U(x) \in B^{m \times q}$$ defined by $latex \[ \begin{array}{rcl} U(x) & = & \partial_u \{ \partial_y g[ y + f^{(1)} (x) R u ] \}_{u=0} \\ & = & \partial_u \{ g^{(1)} [ y + f^{(1)} (x) R u ] \}_{u=0} \\ & = & g^{(2)} (y) f^{(1)} (x) R \end{array} \] $$ $subhead v$$ The $icode rev_hes_sparse$$ argument $icode v$$ has prototype $codei% CppAD::vector< std::set >& %v% %$$ and $icode%v%.size() >= %n%$$. The input values of its elements are not specified (must not matter). Upon return, for $latex j = 0, \ldots , n-1$$, all the elements of $icode%v%[%j%]%$$ are between zero and $icode%q%-1%$$ inclusive. This represents a sparsity pattern for the matrix $latex V(x) \in B^{n \times q}$$ defined by $latex \[ \begin{array}{rcl} V(x) & = & \partial_u [ \partial_x (g \circ f) ( x + R u ) ]_{u=0} \\ & = & \partial_u [ (g \circ f)^{(1)}( x + R u ) ]_{u=0} \\ & = & (g \circ f)^{(2)}( x ) R \\ & = & f^{(1)} (x)^\R{T} g^{(2)} ( y ) f^{(1)} (x) R + \sum_{i=1}^m [ g^{(1)} (y) ]_i \; f_i^{(2)} (x) R \\ & = & f^{(1)} (x)^\R{T} U(x) + \sum_{i=1}^m S(x)_i \; f_i^{(2)} (x) R \end{array} \] $$ $head clear$$ User atomic functions hold onto static work space in order to increase speed by avoiding system memory allocation calls. The function call $codei% user_atomic<%Base%>::clear() %$$ makes to work space $cref/available/ta_available/$$ to for other uses by the same thread. This should be called when you are done using the user atomic functions for a specific value of $icode Base$$. $subhead Restriction$$ The user atomic $code clear$$ routine cannot be called while in $cref/parallel/ta_in_parallel/$$ execution mode. $children% example/atomic/old_reciprocal.cpp% example/atomic/old_usead_1.cpp% example/atomic/old_usead_2.cpp% example/atomic/old_tan.cpp% example/atomic/old_mat_mul.cpp %$$ $head Example$$ $subhead Simple$$ The file $cref old_reciprocal.cpp$$ contains the simplest example and test of a user atomic operation. $subhead Use AD$$ The examples $cref old_usead_1.cpp$$ and $cref old_usead_2.cpp$$ use AD to compute the derivatives inside a user defined atomic function. This may have the advantage of reducing the size of the tape, because a repeated section of code would only be taped once. $subhead Tangent Function$$ The file $cref old_tan.cpp$$ contains an example and test implementation of the tangent function as a user atomic operation. $subhead Matrix Multiplication$$ The file $cref old_mat_mul.cpp$$ contains an example and test implementation of matrix multiplication a a user atomic operation. $end ------------------------------------------------------------------------------ */ # include # include // needed before one can use CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL # include namespace CppAD { // BEGIN_CPPAD_NAMESPACE /*! \file old_atomic.hpp user defined atomic operations. */ /*! \def CPPAD_USER_ATOMIC(afun, Tvector, forward, reverse, for_jac_sparse, rev_jac_sparse, rev_hes_sparse ) Defines the function afun(id, ax, ay) where \c id is \c ax and \c ay are vectors with AD elements. \par Tvector the Simple Vector template class for this function. \par Base the base type for the atomic operation. \par afun name of the CppAD defined function that corresponding to this operation. Note that \c afun, preceeded by a pound sign, is a version of \c afun with quotes arround it. \par forward name of the user defined function that computes corresponding results during forward mode. \par reverse name of the user defined function that computes corresponding results during reverse mode. \par for_jac_sparse name of the user defined routine that computes corresponding results during forward mode jacobian sparsity sweeps. \par rev_jac_sparse name of the user defined routine that computes corresponding results during reverse mode jacobian sparsity sweeps. \par rev_hes_sparse name of the user defined routine that computes corresponding results during reverse mode Hessian sparsity sweeps. \par memory allocation Note that old_atomic is used as a static object, so its objects do note get deallocated until the program terminates. */ # define CPPAD_USER_ATOMIC( \ afun , \ Tvector , \ Base , \ forward , \ reverse , \ for_jac_sparse , \ rev_jac_sparse , \ rev_hes_sparse \ ) \ inline void afun ( \ size_t id , \ const Tvector< CppAD::AD >& ax , \ Tvector< CppAD::AD >& ay \ ) \ { CPPAD_ASSERT_FIRST_CALL_NOT_PARALLEL; \ static CppAD::old_atomic fun( \ #afun , \ forward , \ reverse , \ for_jac_sparse , \ rev_jac_sparse , \ rev_hes_sparse \ ); \ fun(id, ax, ay); \ } /// link so that user_atomic::clear() still works template class user_atomic : public atomic_base { }; /*! Class that actually implements the afun(id, ax, ay) calls. A new old_atomic object is generated each time the user invokes the CPPAD_USER_ATOMIC macro; see static object in that macro. */ template class old_atomic : public atomic_base { public: /// disable old_atomic::clear(void) static void clear(void) { CPPAD_ASSERT_KNOWN( false, "Depreacted API uses user_atomic::clear()" ); } /// type for user routine that computes forward mode results typedef bool (*F) ( size_t id , size_t k , size_t n , size_t m , const vector& vx , vector& vy , const vector& tx , vector& ty ); /// type for user routine that computes reverse mode results typedef bool (*R) ( size_t id , size_t k , size_t n , size_t m , const vector& tx , const vector& ty , vector& px , const vector& py ); /// type for user routine that computes forward mode Jacobian sparsity typedef bool (*FJS) ( size_t id , size_t n , size_t m , size_t q , const vector< std::set >& r , vector< std::set >& s ); /// type for user routine that computes reverse mode Jacobian sparsity typedef bool (*RJS) ( size_t id , size_t n , size_t m , size_t q , vector< std::set >& r , const vector< std::set >& s ); /// type for user routine that computes reverse mode Hessian sparsity typedef bool (*RHS) ( size_t id , size_t n , size_t m , size_t q , const vector< std::set >& r , const vector& s , vector& t , const vector< std::set >& u , vector< std::set >& v ); private: /// id value corresponding to next virtual callback size_t id_; /// user's implementation of forward mode const F f_; /// user's implementation of reverse mode const R r_; /// user's implementation of forward jacobian sparsity calculations const FJS fjs_; /// user's implementation of reverse jacobian sparsity calculations const RJS rjs_; /// user's implementation of reverse Hessian sparsity calculations const RHS rhs_; public: /*! Constructor called for each invocation of CPPAD_USER_ATOMIC. Put this object in the list of all objects for this class and set the constant private data f_, r_, fjs_, rjs_, rhs_. \param afun is the user's name for the AD version of this atomic operation. \param f user routine that does forward mode calculations for this operation. \param r user routine that does reverse mode calculations for this operation. \param fjs user routine that does forward Jacobian sparsity calculations. \param rjs user routine that does reverse Jacobian sparsity calculations. \param rhs user routine that does reverse Hessian sparsity calculations. \par This constructor can not be used in parallel mode because atomic_base has this restriction. */ old_atomic(const char* afun, F f, R r, FJS fjs, RJS rjs, RHS rhs) : atomic_base(afun) // name = afun , f_(f) , r_(r) , fjs_(fjs) , rjs_(rjs) , rhs_(rhs) { this->option( atomic_base::set_sparsity_enum ); } /*! Implement the user call to afun(id, ax, ay). \tparam ADVector A simple vector class with elements of type AD. \param id extra information vector that is just passed through by CppAD, and possibly used by user's routines. \param ax is the argument vector for this call, ax.size() determines the number of arguments. \param ay is the result vector for this call, ay.size() determines the number of results. */ template void operator()(size_t id, const ADVector& ax, ADVector& ay) { // call atomic_base function object this->atomic_base::operator()(ax, ay, id); return; } /*! Store id for next virtual function callback \param id id value corresponding to next virtual callback */ virtual void set_id(size_t id) { id_ = id; } /*! Link from old_atomic to forward mode \copydetails atomic_base::forward */ virtual bool forward( size_t p , size_t q , const vector& vx , vector& vy , const vector& tx , vector& ty ) { CPPAD_ASSERT_UNKNOWN( tx.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( ty.size() % (q+1) == 0 ); size_t n = tx.size() / (q+1); size_t m = ty.size() / (q+1); size_t i, j, k, ell; vector x(n * (q+1)); vector y(m * (q+1)); vector empty; // old_atomic interface can only handel one order at a time // so must just throuh hoops to get multiple orders at one time. bool ok = true; for(k = p; k <= q; k++) { for(j = 0; j < n; j++) for(ell = 0; ell <= k; ell++) x[ j * (k+1) + ell ] = tx[ j * (q+1) + ell ]; for(i = 0; i < m; i++) for(ell = 0; ell < k; ell++) y[ i * (k+1) + ell ] = ty[ i * (q+1) + ell ]; if( k == 0 ) ok &= f_(id_, k, n, m, vx, vy, x, y); else ok &= f_(id_, k, n, m, empty, empty, x, y); for(i = 0; i < m; i++) ty[ i * (q+1) + k ] = y[ i * (k+1) + k]; } return ok; } /*! Link from old_atomic to reverse mode \copydetails atomic_base::reverse */ virtual bool reverse( size_t q , const vector& tx , const vector& ty , vector& px , const vector& py ) { CPPAD_ASSERT_UNKNOWN( tx.size() % (q+1) == 0 ); CPPAD_ASSERT_UNKNOWN( ty.size() % (q+1) == 0 ); size_t n = tx.size() / (q+1); size_t m = ty.size() / (q+1); bool ok = r_(id_, q, n, m, tx, ty, px, py); return ok; } /*! Link from forward Jacobian sparsity sweep to old_atomic \copydetails atomic_base::for_sparse_jac */ virtual bool for_sparse_jac( size_t q , const vector< std::set >& r , vector< std::set >& s ) { size_t n = r.size(); size_t m = s.size(); bool ok = fjs_(id_, n, m, q, r, s); return ok; } /*! Link from reverse Jacobian sparsity sweep to old_atomic. \copydetails atomic_base::rev_sparse_jac */ virtual bool rev_sparse_jac( size_t q , const vector< std::set >& rt , vector< std::set >& st ) { size_t n = st.size(); size_t m = rt.size(); bool ok = rjs_(id_, n, m, q, st, rt); return ok; } /*! Link from reverse Hessian sparsity sweep to old_atomic \copydetails atomic_base::rev_sparse_hes */ virtual bool rev_sparse_hes( const vector& vx, const vector& s , vector& t , size_t q , const vector< std::set >& r , const vector< std::set >& u , vector< std::set >& v ) { size_t m = u.size(); size_t n = v.size(); CPPAD_ASSERT_UNKNOWN( r.size() == n ); CPPAD_ASSERT_UNKNOWN( s.size() == m ); CPPAD_ASSERT_UNKNOWN( t.size() == n ); // // old interface used id instead of vx bool ok = rhs_(id_, n, m, q, r, s, t, u, v); return ok; } }; } // END_CPPAD_NAMESPACE # endif